How can the same action lead to a civil and a criminal case?

It can be based on the circumstances. Example if the person robs a 7-11 with a weapon, in some states it is a higher charge, if they use the weapon as in hit the cashier, discharge the weapon. It could be criminal. Prior arrest records of convictions also matter.

Crossing a state line can bring federal charges.

Usually, the level of the crime has to do with acts within the process of the act.

Especially if they harm someone in the act. Kidnap a hostage, carjack, or become unstable and threaten the hostage. Check your local or state statutes and add more "Happenings" to the event you can follow the trail up.

Something happened to raise the charge. Maybe you take a car because they owe you money, unknown to you it has a sleeping child inside.

Another event might be your stock investor Advisory informed you that you would be wealthy with this investment. After the gain, the investor added so many charges to your account, and these were unexpected. You file a civil complaint against him. During depositions your attorney feels this is a illegal act, and many people have suffered from making the purchase. He contacts the DA office and it becomes criminal after they feel it meets the requirement of the law to prosecute.

You decide to damage somebodies brain and mental stability on purpose. The family can sue you, and it is assault or against the law in some way